Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation

In order to get an efficient image representation we introduce a new adaptive Haar wavelet transform, called Tetrolet Transform. Tetrolets are Haar-type wavelets whose supports are tetrominoes which are shapes made by connecting four equal-sized squares. The corresponding fast filter bank algorithm is simple but very effective. In every level of the filter bank algorithm we divide the low-pass image into 4 × 4 blocks. Then in each block we determine a local tetrolet basis which is adapted to the image geometry in this block. An analysis of the adaptivity costs leads to modified versions of our method. Numerical results show the strong efficiency of the tetrolet transform for image approximation.